12 papers
The algebra of Krom logic programs
Christian Antić
This paper investigates the algebraic structure of Krom logic programs, consisting only of facts and rules with at most one body atom. We show that sequential composition endows th…
Set-like operations on propositional logic programs
Christian Antić
Composition and decomposition of logic programs have been studied extensively in the context of modularity, and decomposing a program along the dependency structure of its atoms --…
Algebraic anti-unification
Christian Antić
Abstraction is key to human and artificial intelligence as it allows one to identify common structure in otherwise distinct objects or situations. Anti-unification (or generalizati…
Neural logic programs and neural nets
Christian Antić
Neural-symbolic integration aims to combine the connectionist subsymbolic with the logical symbolic approach to artificial intelligence. In this paper, we first define the answer s…
Logic-based analogical proportions
Christian Antić
The author has recently introduced an abstract algebraic framework of analogical proportions within the general setting of universal algebra. The purpose of this paper is to lift t…
Analogical proportions II
Christian Antić
Analogical reasoning is the ability to detect parallels between two seemingly distant objects or situations, a fundamental human capacity used for example in commonsense reasoning,…
Similarity-based analogical proportions
Christian Antić
The author has recently introduced abstract algebraic frameworks of analogical proportions and similarity within the general setting of universal algebra. The purpose of this paper…
Bilingual analogical proportions via hedges
Christian Antić
Analogical proportions are expressions of the form `` is to what is to '' at the core of analogical reasoning which itself is at the core of human and artificial inte…
Logic-based similarity
Christian Antić
This paper develops a {\em qualitative} and logic-based notion of similarity from the ground up using only elementary concepts of first-order logic centered around the fundamental…
Algebraic characterizations of least model and uniform equivalence of propositional Krom logic programs
Christian Antić
This research note provides algebraic characterizations of the least model, subsumption, and uniform equivalence of propositional Krom logic programs.
Proportoids
Christian Antić
Analogical proportions are expressions of the form `` is to what is to '' at the core of analogical reasoning, which itself is at the core of artificial intelligence.…
Sequential composition of answer set programs
Christian Antić
This paper contributes to the mathematical foundations of logic programming by introducing and studying the sequential composition of answer set programs. On the semantic side, we…